Is there a manageable formula or set of formulas or simple algorithms that approximate stellar luminosity and effective temperature (or radius) as a function of stellar age?

I'm aware that accurate modeling of these attributes is complex and is determined by many factors; what I'm looking for is something that serves as a decent approximation of the sort used in numerous illustrations or applets that show example "paths" taken by representative stars as they trace their evolution across the H-R diagram.

This is not really an answer to your question, but Java applets can be easily disassembled into Java source code using freely available tools. The results are often surprisingly readable. Or you could simply see if the applet is open source, or email the author to ask.
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Ben CrowellJul 22 '11 at 4:07

maybe the links here PSE that relates a star's Period of Rotation-Mass-Age, can help you
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Helder VelezJul 22 '11 at 10:16

Well, everything can be approximated by a multivariate polynomial, one way or another. I believe my old stellar astrophysics textbook, Kippenhahn and Wiegert, went through it in depth. I don't have access to my copy at the moment, though.
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AndrewJul 22 '11 at 20:54

Not quite what I was looking for. I'll happily trade accuracy for an approximation in a form that captures the major thrust of the underlying events.
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raxacoricofallapatoriusJul 23 '11 at 15:39

An extensive and homogenous database of stellar evolution models for
masses between 0.8 and 120 solar masses and metallicities from Z=0.001
to 0.1 is available. In general the models include evolutionary phases
from the main sequence up to either the end of carbon burning for
massive stars, the early asymptotic giant branch phase for
intermediate-mass stars, or core helium flash for low-mass stars.
Pre-main sequence tracks, both canonical (i.e. evolved at constant
mass) and accretion scenarios are also provided, as well as horizontal
banches for low-mass stars. Predictions regarding the spectral
evolution of massive stars can further be obtained from the so-called
"combined stellar structure and atmosphere models" (CoStar).

In addition to the evolutionary grids we also provide Fortran codes
for the calculation of isochrones and stellar population burst models.

Finally, references are also given to the serie of papers on stellar
models with rotation.

With that being said, it's not perfect. We don't know about variations in luminosity - the Sun's luminosity has varied in cycles (the 11-year sunspot cycle is one of them - but there may be others that last hundreds of years too - that could explain things like the Maunder Minimum). This is something that we might learn more of from Kepler telescope data on stellar oscillation, as described in the Chaplin et al. (2011) paper

It also depends on the angle that we view the star. And we may have to correct our zero-age main sequence luminosities too (since some stars can be unusually bright at zero-age). E.g. Altair is unusually bright for its temperature, but several papers have concluded that it's ZAMS rather than subgiant (it's rotating unusually fast, which is something you mostly see in new stars)

What I'm looking for is something more compact, say one or two simple functions. It can be a very rough approximation, but I'm wondering if there there is such a thing, and whether it's at all useful in generating even an approximate picture of how stars evolve on the H-R diagram. The answer may be that no such thing exists: that nothing that simple really captures the picture.
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raxacoricofallapatoriusSep 22 '11 at 14:37